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Other ways to solve analogy problems --- spaces

This is not necessary for Finals. I've included it because it's interesting to compare it with Evans' program. They use very different representations to solve seemingly similar problems.

A Model for Analogical Reasoning, by Rumelhart and Abrahamson, in Cognitive Psychology, volume 5 (1973). They consider how we conceptualise animals, and offer evidence to suggest that we consider them as points on a 3-dimensional graph whose axes are ferocity, size, and humanness.

Further, they ask how we solve analogy problems such as ``Giraffe is to Chimpanzee as Bear is to (Gorilla, Elephant, Dog, Camel, Lion)''.

Consider each of the animals as a point in this 3-dimensional space. Then you can draw a line from Giraffe to Chimpanzee. (In Evans' terms, this would be the rule connecting A and B). If you draw a line of the same length and direction from Bear, this gives you the ideal result. (In Evans' terms, this is applying the A to B rule to C). The best answer out of the five choices is the animal from (Gorilla, Elephant, Dog, Camel, Lion) which is nearest to this point.

The authors conjecture that the probability of subjects picking an answer decreases as its distance from the ideal solution increases according to a choice law.

So here we have another mechanism which, in abstract terms is similar to Evans' (find a rule; apply it again; pick the best result), but where the relations are represented in quite a different way.

Jocelyn Paine
Tue Jun 3 11:33:37 BST 1997